I've had two friends announce in the last week that they've been severed from big companies. It appears to be because of the cancellation of government contracts. I doubt they are alone. I also doubt that we'll see job statistics showing us anywhere near accurate numbers for this.
Job statistics have been becoming less accurate _in the short term_ because of survey response rates (down and slow) but it's _really_ hard to fake numbers. They can get less accurate but it would be a massive conspiracy to intentionally skew them.
I think they are planning to do away with monthly jobs reports. So far as skewing numbers - that's the game plan across way too much of this administration. It's why so many are saying we can't trust anything coming out of the White House or its departments/agencies.
Markets will react strongly if they actually do that. Private reports are not sufficient for the purposes used. They are only afraid of one thing and that's the markets.